They say the eyes are the window to the soul. Well, in a film, the eyes are the first place an audience member looks, the second is the hands. We are trying to connect with the character on screen. The eyes tell us so much about what the character is thinking. It is so important to spend enough time making sure you put enough detail into the eyes and brows. What am I talking about when I say detail? When I was animating on Mike Wazowski, we did some reference to really see how the eye moved. I took lots of notes on the live action footage and applied it to an animated eye. Some of the things I learned were how the lid moves with the eyes, the different kinds of blinks an eye is capable of and many other things. For instance, a lot of the time when your eye makes a bid move fro left to right, your eye lid half closes. We learned that you need to shape the eye lid to help sell eye direction. There is a virtual laundry list of thing to make a cg eye look believable. What I am saying is, do you homework and look at how your eye works and try to get it into your work. In order to get better, its so important to take the time and really figure out how things work.
Here are few tidbits to remember about the eye.
Blinks: No matter how slow or quick they are, remember to add a little cushion at the top of the blink. When you don’t and it just stops, it looks a bit mechanical.
Eye Darts: Eye darts vary. Sometimes they are one frame, mostly two frames. But there is no rule. The most important thing to remember about the eye dart is to think why you are doing it. Its usually nice to animate eye darts in a particular pattern. For instance if I was doing a close up, I might dart the eye left to right, then down, then back up. This would be because my character is looking at the left eye, then the right, then looking at the mouth. Its all about thought process.
Hope this helps a bit.